Dst stands for "Disturbance - storm time". It is one of three indices that measures the worldwide deviation of the Earth's magnetic field from quiet conditions. The first is the auroral electrojet (AE) index, and it measures geomagnetic field activity at high latitudes. The second is the 3-hour planetary K (Kp) index, and it measures geomagnetic field activity at mid latitudes. The third is the Dst index, and it measures geomagnetic field activity at low latitudes.
As expected, there is correlation between all three indices. But being measured in different latitude sectors, the correlation is not perfect. Furthermore, there can be some overlap in the indices as processes occurring at high and low latitudes, as moniored by the AE and Dst indices, can influence the mid latitudes where the Kp index is recorded.
In general, high Kp and AE indices equate to a negative Dst index. When this happens, propagation at high and mid latitudes can degrade. But propagation at low latitudes can be enhanced.
You can find a more detailed description here: http://pluto.space.swri.edu/IMAGE/glossary/dst.html
Carl K9LA